I have been given a job to organise a tournament for the local tennis association.

The following information is available:

All matches are singles.

All players have to play all other players once

Individual matches take exactly a half an hour each

There are only four tables available

Six people register in advance for the tournament.

Answer the following questions about the tournament:

1. If no other people register, how many games will be played in the tournament and how long will the tournament take?

2. Last year nine people registered at the last minute. If this happens again this year, there will be a total of 15 people playing. If this happens again, how many singles matches will I need to schedule?

3. Complete this table for a similar type of tournament for the numbers of players given.

Number of players

Number of matches

2

3

4

5

6

15

100

n

4. If I use all four tables, as often as possible, how long will the tournament take to play with the fifteen players?

5. If I can find four more tables, for fifteen players what changes can occur?